M-Files

Algoritmo della secante

Un metodo iterativo per la risoluzione dell'algoritmo della secante

%function [p1,err,k,y]=secant(f,p0,p1,delta,epsilon,max1)
%Input - f is the object function input as a string 'f'
%      - p0 and p1 are the initial approximations to a zero of f
%     - delta is the tolerance for p1
%     - epsilon is the tolerance for the function values y
%     - max1 is the maximum number of iterations
%Output - p1 is the secant method approximation to the zero
%      - err is the error estimate for p1
%      - k is the number of iterations
%      - y is the function value f(p1)

while 1

   clear, clf,clc
   fprintf( '\n============================================\n' );
   fprintf( ' Secant Method \n' );

   while 1
      fprintf( ' \n The absciss extremes a and b (a < b)')
      fprintf( ' \n a = ');  a = input('');
      fprintf( ' b = ');  b = input('');
      if a < b;  break; end
      fprintf( ' \n a should be less than b! ')
      fprintf( ' \n Repeat your input for a and b! ')
   end

   fprintf( ' \n Now the function is plotted \n')
   x=a:0.1:b;
   f = feval('f306',x);
   plot(x, f, 'b-');
   centaxes
   hold on;

   fprintf( '** Give the Po, first initial abscissa value approximation to a zero of f:\n');
   p0 = input('Initial approximation Po = ');

   fprintf( '** Give the P1, second initial abscissa value approximation to a zero of f:\n');
   p1 = input('Initial approximation P1 = ');

   while 1
      fprintf( '\n Input the tolerance value for P1, delta = ')
      delta = input('');
      if delta < 1 & delta > 0;  break; end
      fprintf( ' \n Delta should be greater than 0 and less than 1!!! ')
      fprintf( ' \n Repeat your input for tolerance value! ')
   end

   while 1
      fprintf( '\n Input the tolerance value for the function Y values, epsilon = ')
      epsilon = input('');
      if epsilon < 1 & epsilon > 0;  break; end
      fprintf( ' \n Epsilon should be greater than 0 and less than 1!!! ')
      fprintf( ' \n Repeat your input for tolerance value! ')
   end

   while 1
      fprintf( '\n Input the maximum number of iterations, N_max = ')
      max1 = input('');
      if max1 > 1;  break; end
      fprintf( ' \n The number of iterations should be greater than 1!!! ')
      fprintf( ' \n Repeat your input for the number of iterations value! ')
   end

   for k=1:max1
    p2=p1-feval('f306',p1)*(p1-p0)/(feval('f306',p1)-feval('f306',p0));
    err=abs(p2-p1);
    relerr=2*err/(abs(p2)+delta);
    p0=p1;
    p1=p2;
    y=feval('f306',p1);
    if (err<delta)|(relerr<delta)|(abs(y)<epsilon),break,end
   end

   fprintf('\n==============RESULTS================')

   fprintf('\n P1 is the Secant approximation to zero = %12.6f', p1);
   fprintf('\n Err is the error estimate for P1 = %12.6f', err);
   fprintf('\n K is the number of iterations = %u', k);
   fprintf('\n Y is the function value f(P1) = %12.6f', y);

   fprintf('\n============================================')
   kont1 = input( 'Type 1 to continue, or 0 to stop: ' );
   if kont1 == 0, break; end
end

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